Basic Math Examples

$\frac{t^{2} - 1}{3 t - 3} \div (t + 1)$

Step 1

Rewrite the division as a fraction.

$\frac{\frac{t^{2} - 1}{3 t - 3}}{t + 1}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$\frac{t^{2} - 1}{3 t - 3} \cdot \frac{1}{t + 1}$

Step 3

Simplify the numerator.

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Step 3.1

Rewrite $1$ as $1^{2}$ .

$\frac{t^{2} - 1^{2}}{3 t - 3} \cdot \frac{1}{t + 1}$

Step 3.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = t$ and $b = 1$ .

$\frac{(t + 1) (t - 1)}{3 t - 3} \cdot \frac{1}{t + 1}$

Step 4

Simplify terms.

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Step 4.1

Factor $3$ out of $3 t - 3$ .

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Step 4.1.1

Factor $3$ out of $3 t$ .

$\frac{(t + 1) (t - 1)}{3 (t) - 3} \cdot \frac{1}{t + 1}$

Step 4.1.2

Factor $3$ out of $- 3$ .

$\frac{(t + 1) (t - 1)}{3 (t) + 3 (- 1)} \cdot \frac{1}{t + 1}$

Step 4.1.3

Factor $3$ out of $3 (t) + 3 (- 1)$ .

$\frac{(t + 1) (t - 1)}{3 (t - 1)} \cdot \frac{1}{t + 1}$

Step 4.2

Cancel the common factor of $t + 1$ .

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Step 4.2.1

Cancel the common factor.

$\frac{(t + 1) (t - 1)}{3 (t - 1)} \cdot \frac{1}{t + 1}$

Step 4.2.2

Rewrite the expression.

$\frac{t - 1}{3 (t - 1)}$

Step 4.3

Cancel the common factor of $t - 1$ .

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Step 4.3.1

Cancel the common factor.

$\frac{t - 1}{3 (t - 1)}$

Step 4.3.2

Rewrite the expression.

$\frac{1}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{3}$

Decimal Form:

$0.\overline{3}$